Yemen's Houthi rebels have claimed responsibility for missile attacks on the Saudi Arabia cities of Jazan and Yanbu, marking a widening of conflict in the Middle East.

The Iran-backed group's military spokesperson Yahya Sare said in a statement that the group carried out operations targeting Saudi Aramco facilities in Jazan and Yanbu.

Greek security sources said that air defence systems in Saudi Arabia had intercepted two ballistic missiles from Yemen on Saturday, which were targeting oil refineries in Yanbu.

Video posted to social media suggested the Aramco oil refinery in Jazan had been hit.

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The Houthis had accused Saudi Arabia — a US ally — of a "dangerous escalation" after Riyadh struck military targets belonging to the Houthis on Friday, following the rebels announcing a maritime blockade of the top oil producer and hitting Riyadh's ships in the Red Sea.

The Iran-backed group claimed attacks on two Saudi ships earlier this week, with Saudi Arabia confirming one of the attacks in the Red Sea.

Riyadh did not immediately comment on the newest strikes, but its civil defence agency issued brief warnings to residents in the city, as well as Yanbu, earlier on Saturday.

The Saudi-backed Yemeni government air force also carried out air strikes on Houthi missile and drone launch sites and arms depots in the Marib and al-Jawf provinces, two military officials said.

The officials said the strikes were among the first offensive operations launched by the Yemeni government against the Houthis amid the latest conflict.

Talks 'most serious that we've seen them'

Donald Trump says talks with Iran are continuing. (AP: Rod Lamkey Jr)

This flare-up marks a new front in a war that has engulfed the Middle East region following US-Israeli strikes on Tehran in February, and comes on top of Iran's parallel blockade of the Strait of Hormuz, Saudi Arabia's only other maritime route.

The key waterway of the Strait of Hormuz, the entrance to the Gulf, has so far been the focus of a war that has killed thousands over almost five months, stoked global inflation and fanned fears of an economic downturn.

The escalation came after US President Donald Trump said he would hold off on a major operation because Iran was now getting "serious" in talks with Washington.

The US military broke its daily announcement of fresh strikes on the Islamic republic on Saturday, following 13 nights in a row hitting military targets there.

"We are talking to them," Mr Trump told reporters at the White House on Friday.

"I think they're being serious. I think … they are being by far the most serious that we've seen them, but that doesn't mean we get there."

Asked what the exit strategy was for the Iran war, Mr Trump said there was a "military exit where we just keep going just the way we are, and we can even make it a heavier dose, and it's knocking out everything they have. Or there's a smarter strategy that you make a deal".

He said Iran had a choice between making a deal or facing a "much higher level" of strikes after nearly two weeks of US attacks that left the ceasefire in tatters.

"We're locked and loaded. We're ready to go," Mr Trump said.

He added that he did not know what the "tipping point" would be for a decision, but reiterated that Iran being close to developing a nuclear weapon would be a red line.

Russia, China not arming Iran, Trump says

Mr Trump also insisted that Russia and China were not arming Iran, despite reports both were feeding Tehran intelligence to target US forces.

US and Iran trade strikes

The strikes came after US President Donald Trump vowed "major military punishment" for Tehran and its Houthi allies in Yemen over moves to block a second major international shipping route.

"President Xi [Jinping] said he will not partake, and President [Vladimir] Putin said the same thing … I trust them," Mr Trump told reporters.

"I don't think they'd want to have me disappointed."

Chinese Foreign Minister Wang Yi has met his Iranian counterpart Abbas Araghchi in Kyrgyzstan, calling for a memorandum of understanding aimed at easing tensions in the Middle East and the Gulf region, Chinese state news agency Xinhua reported.

ABC/wires